O'Neill had faced calls to be more expansive going into the game following a goalless draw in Copenhagen on Saturday, but quickly faced criticism after the defeat in Dublin for lacking caution, as Eriksen struck three goals and Nicklas Bendtner finished off the scoring from the spot late on.
It as a much different story in the Danish camp, however, as manager Age Hareide and his players celebrated a major victory for Denmark, once that propels them to the World Cup for the first time since 2010.
"Clueless. Absolutely clueless. To allow the players like they have the space, the time, in the key areas of the pitch, even the substitutions, Ciaran Clark coming off - unless he's injured - with Ward going to centre-half, I really don't know what I've witnessed".
In the first leg against Denmark, his side had just 28% possession, while Southampton striker Shane Long, who has 17 worldwide goals, started on the bench for both games.
Hareide said: "The whole team did well, played well and scored a lot of goals and we are in Russian Federation".
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The hosts upped the tempo for the rest of the first half, but they were unable to find the equaliser as they went into the break trailing.
"We had two great chances to make it 2-0".
Meanwhile, Eriksen was delighted to get three goals and help his nation reach the World Cup in Russian Federation. We are very much looking forward to it.
The result sees Denmark cement their place at next summer's World Cup from the European qualifiers, alongside Sweden, Switzerland and Croatia.
"We can not ignore that Eriksen delivered an incredible performance and probably played his best worldwide game, in my opinion", Bendtner told reporters. I don't think he will, I think he'll pick Long because Murphy had a tough game the other night. "They are technically better than us and had a world-class player [Eriksen] in their team". I take the more clinical shot rather than passing.